Noncommutative Differential Forms on the kappa-deformed Space

Abstract

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

to appear in J. Phys. A: Math. Theor

References in corpus (15)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• Kappa-Minkowski space-time and the star product realizations
• New realizations of Lie algebra kappa-deformed Euclidean space
• Twisted Statistics in kappa-Minkowski Spacetime
• Covariant realizations of kappa-deformed space
• Gauge theories on the kappa-Minkowski spacetime
• From noncommutative kappa-Minkowski to Minkowski space-time
• Lie algebraic Noncommutative Gravity
• Generalized kappa-deformed spaces, star-products, and their realizations
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• kappa-deformed Spacetime From Twist
• Gauge Generators, Transformations and Identities on a Noncommutative Space
• Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
• Gauge Symmetries on $\theta$-Deformed Spaces

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• $\kappa$-deformed Dirac Equation
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• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Effects of Noncommutativity on the Black Hole Entropy
• Maxwell's equations on the $\kappa$-Minkowski spacetime and Electric-Magnetic duality
• Relativistic quantum heat engine from uncertainty relation standpoint
• Differential algebras on kappa-Minkowski space and action of the Lorentz algebra
• Uniformly accelerating observer in $\kappa$-deformed space-time
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• Bound on efficiency of heat engine from uncertainty relation viewpoint
• Differential forms and k-Minkowski spacetime from extended twist
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• MICZ Kepler Systems in Noncommutative Space and Duality of Force Laws
• The Weyl realizations of Lie algebras and left-right duality
• Effect of Non-commutativity of space-time on Thermodynamics of Photon gas
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time
• Maximal acceleration in non-commutative space-time and its implications
• Quantisation of $\kappa$-deformed Dirac equation
• Generalization of Weyl realization to a class of Lie superalgebras